162,155 research outputs found
Bifurcations from families of periodic solutions in piecewise differential systems
Consider a differential system of the form where
and are piecewise
functions and -periodic in the variable . Assuming that the unperturbed
system has a -dimensional submanifold of periodic solutions
with , we use the Lyapunov-Schmidt reduction and the averaging theory to
study the existence of isolated -periodic solutions of the above
differential system
Characteristic ideals and Iwasawa theory
Let \L be a non-noetherian Krull domain which is the inverse limit of
noetherian Krull domains \L_d and let be a finitely generated \L-module
which is the inverse limit of \L_d-modules . Under certain hypotheses
on the rings \L_d and on the modules , we define a pro-characteristic
ideal for in \L, which should play the role of the usual characteristic
ideals for finitely generated modules over noetherian Krull domains. We apply
this to the study of Iwasawa modules (in particular of class groups) in a
non-noetherian Iwasawa algebra \Z_p[[\Gal(\calf/F)]], where is a function
field of characteristic and \Gal(\calf/F)\simeq\Z_p^\infty.Comment: 15 pages, substantial chenges in exposition, new section 2.
Connexins: synthesis, post-translational modifications, and trafficking in health and disease
Connexins are tetraspan transmembrane proteins that form gap junctions and facilitate direct intercellular communication, a critical feature for the development, function, and homeostasis of tissues and organs. In addition, a growing number of gap junction-independent functions are being ascribed to these proteins. The connexin gene family is under extensive regulation at the transcriptional and post-transcriptional level, and undergoes numerous modifications at the protein level, including phosphorylation, which ultimately affects their trafficking, stability, and function. Here, we summarize these key regulatory events, with emphasis on how these affect connexin multifunctionality in health and disease
On the expected number of perfect matchings in cubic planar graphs
A well-known conjecture by Lov\'asz and Plummer from the 1970s asserted that
a bridgeless cubic graph has exponentially many perfect matchings. It was
solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the other
hand, Chudnovsky and Seymour (Combinatorica 2012) proved the conjecture in the
special case of cubic planar graphs. In our work we consider random bridgeless
cubic planar graphs with the uniform distribution on graphs with vertices.
Under this model we show that the expected number of perfect matchings in
labeled bridgeless cubic planar graphs is asymptotically , where
and is an explicit algebraic number. We also
compute the expected number of perfect matchings in (non necessarily
bridgeless) cubic planar graphs and provide lower bounds for unlabeled graphs.
Our starting point is a correspondence between counting perfect matchings in
rooted cubic planar maps and the partition function of the Ising model in
rooted triangulations.Comment: 19 pages, 4 figure
Oscillatory and Fourier Integral operators with degenerate canonical relations
We mostly survey results concerning the boundedness of oscillatory and
Fourier integral operators. This article does not intend to give a broad
overview; it mainly focusses on a few topics directly related to the work of
the authors.Comment: 37 pages, to appear in Publicacions Mathematiques (special issue,
Proceedings of the 2000 El Escorial Conference in Harmonic Analysis and
Partial Differential Equations
Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis
We propose a modelling framework to analyse the stochastic behaviour of
heterogeneous, multi-scale cellular populations. We illustrate our methodology
with a particular example in which we study a population with an
oxygen-regulated proliferation rate. Our formulation is based on an
age-dependent stochastic process. Cells within the population are characterised
by their age. The age-dependent (oxygen-regulated) birth rate is given by a
stochastic model of oxygen-dependent cell cycle progression. We then formulate
an age-dependent birth-and-death process, which dictates the time evolution of
the cell population. The population is under a feedback loop which controls its
steady state size: cells consume oxygen which in turns fuels cell
proliferation. We show that our stochastic model of cell cycle progression
allows for heterogeneity within the cell population induced by stochastic
effects. Such heterogeneous behaviour is reflected in variations in the
proliferation rate. Within this set-up, we have established three main results.
First, we have shown that the age to the G1/S transition, which essentially
determines the birth rate, exhibits a remarkably simple scaling behaviour. This
allows for a huge simplification of our numerical methodology. A further result
is the observation that heterogeneous populations undergo an internal process
of quasi-neutral competition. Finally, we investigated the effects of
cell-cycle-phase dependent therapies (such as radiation therapy) on
heterogeneous populations. In particular, we have studied the case in which the
population contains a quiescent sub-population. Our mean-field analysis and
numerical simulations confirm that, if the survival fraction of the therapy is
too high, rescue of the quiescent population occurs. This gives rise to
emergence of resistance to therapy since the rescued population is less
sensitive to therapy
Local positivity in terms of Newton-Okounkov bodies
In recent years, the study of Newton-Okounkov bodies on normal varieties has
become a central subject in the asymptotic theory of linear series, after its
introduction by Lazarsfeld-Mustata and Kaveh-Khovanskii. One reason for this is
that they encode all numerical equivalence information of divisor classes (by
work of Jow). At the same time, they can be seen as local positivity
invariants, and K\"uronya-Lozovanu have studied them in depth from this point
of view. We determine what information is encoded by the set of all
Newton-Okounkov bodies of a big divisor with respect to flags centered at a
fixed point of a surface, by showing that it determines and is determined by
the numerical equivalence class of the divisor up to negative components in the
Zariski decomposition that do not go through the fixed point.Comment: 10 pages. Comments welcom
Atomic Fermi-Bose mixtures in inhomogeneous and random lattices: From Fermi glass to quantum spin glass and quantum percolation
We investigate atomic Fermi-Bose mixtures in inhomogeneous and random optical
lattices in the limit of strong atom-atom interactions. We derive the effective
Hamiltonian describing the dynamics of the system and discuss its low
temperature physics. We demonstrate possibility of controlling the interactions
at local level in inhomogeneous but regular lattices. Such a control leads to
the achievement of Fermi glass, quantum Fermi spin glass, and quantum
percolation regimes involving bare and/or composite fermions in random
lattices.Comment: minor changes; Physical Review Letters 93, 040401 (2004
Phase-dependent interaction in a 4-level atomic configuration
We study a four-level atomic scheme interacting with four lasers in a
closed-loop configuration with a (diamond) geometry. We
investigate the influence of the laser phases on the steady state. We show
that, depending on the phases and the decay characteristic, the system can
exhibit a variety of behaviors, including population inversion and complete
depletion of an atomic state. We explain the phenomena in terms of multi-photon
interference. We compare our results with the phase-dependent phenomena in the
double- scheme, as studied in [Korsunsky and Kosachiov, Phys. Rev A
{\bf 60}, 4996 (1999)]. This investigation may be useful for developing
non-linear optical devices, and for the spectroscopy and laser-cooling of
alkali-earth atoms.Comment: 4 figure
Extracting Atoms on Demand with Lasers
We propose a scheme that allows to coherently extract cold atoms from a
reservoir in a deterministic way. The transfer is achieved by means of
radiation pulses coupling two atomic states which are object to different
trapping conditions. A particular realization is proposed, where one state has
zero magnetic moment and is confined by a dipole trap, whereas the other state
with non-vanishing magnetic moment is confined by a steep microtrap potential.
We show that in this setup a predetermined number of atoms can be transferred
from a reservoir, a Bose-Einstein condensate, into the collective quantum state
of the steep trap with high efficiency in the parameter regime of present
experiments.Comment: 11 pages, 8 figure
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